16.
We use a combination of analytic and grapher techniques to solve this problem. Depending on the viewing windows chosen,
graphs obtained using NDER may exhibit strange behavior near
x
5
2 because, for example, NDER (
y
, 2)
<
5,000,000 while
y
9
is actually undefined at
x
5
2. The graph of
y
5
}
5
2
4
x
x
1
2
4
2
x
2
2
x
3
}
is shown below.
[
2
5.875, 5.875] by [
2
50, 30]
y
9 5
5
The graph of
y
9
is shown below.
[
2
5.875, 5.875] by [
2
50, 30]
The zero of
y
9
is
x
<
0.215.
y
0 5
5
5
The graph of
y
0
is shown below.
[
2
5.875, 5.875] by [
2
20, 20]
The zero of
x
3
2
6
x
2
1
12
x
2
13
(and hence of
y
0
) is
x
<
3.710.
(a)
Approximately (
2‘
, 0.215]
(b)
Approximately [0.215, 2) and (2,
‘
)
(c)
Approximately (2, 3.710)
(d)
(
2‘
, 2) and approximately (3.710,
‘
)
(e)
Local maximum at
<
(0.215,
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 Spring '08
 GERMAN
 Derivative, Convex function, Types of functions, Intervals Sign

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